On coincidence and common fixed points of nearly densifying mappings (Q5926129)

Let \(A\) be a bounded subset of a metric space \((X,d)\) and \(\alpha(A)\) be the Kuratowski measure of noncompactness of \(A\). A mapping \(f: X\to X\) is said to be nearly densifying if \(\alpha(f(A))<\alpha(A)\) for every bounded and \(f\)-invariant subset \(A\) of \(X\) with \(\alpha(A)> 0\).NEWLINENEWLINENEWLINEIn the present paper the authors establish some coincidence and common fixed point theorems for certain nearly densifying mappings in complete metric spaces. These results unify a lot of previously known theorems.